Just to add to Ian's reply, it's quite surprising how 'accurate' you can get after a bit of practice. A colleague and I used to estimate the size of the gull roost at Pennington on a regular basis. We'd both write the figure down to prevent cheating. Even though numbers were in the thousands we'd usually be within a couple of hundred of each other.
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No one on their death bed ever said they wished they'd spent more time at work. http://bitsnbirds.blogspot.co.uk
Counting of this nature is something of an ‘artform’ and carried out by experienced observers can be remarkably accurate though obviously not exact.
Basically, each flock is counted/estimated and each total is written in a notebook where at the end of the session, those individual flocks are counted up to give an overall total. In the case you refer to, Andy will have filled a few pages in his notebook and taken a considerable amount of time just to count them all up afterwards!
Smaller (manageable) flocks of birds will be counted exact, giving odd or even numbers but larger flocks must take a different, tried and tested, approach. For large flocks you generally count in small numbers first, say each individual up to ten and when you have an idea what ten looks within the whole flock like you can in count tens until you’ve counted them all or for larger flocks once you count (in tens) to 100 you count in 100s until you have counted the lot. This generally gives an even numbered count and can be remarkably accurate though obviously not exact but other than trying to photograph the flock and count later, it’s the only way such flocks can be counted. With experience this can be done very quickly though its best done where the geography permits views long enough to count, so good vantage points with clear vistas are necessary (which is exactly what they have up on the Horwich Moors).
Once you add up all those odd and even flock numbers you get your day’s totals which in Andy’s case came to 63962 but importantly, from 449 flocks (so interestingly an average of 142 per flock!).
Some counting can also be done with ‘clickers’ but for such enormous migration numbers this becomes quite difficult (not just on the thumbs either) and the aforementioned method is best. An example of such counting from my own notebook a few days ago (even though I wrote the wrong month down!!) is attached below, though unfortunately it wasn’t from yesterday’s big day.
I've wondered for some time about the numbers given in the sightings thread. Could someone explain how it's possible to come up with a number as precise as 63962 redwings? I watched them coming over Mellor Moor a few years ago and hundreds were passing above me, to the right and to the left so I couldn't have even estimated the total to the nearest thousand. If it's an estimate based on a sample then quoting to the nearest 100 or 1000 would seem more appropriate. As a science teacher I had to stress the idea of significant figures in all calculations.